Orienting Yourself The Use of Coordinates Class 9 Extra Questions Maths Chapter 1

By using Extra Questions for Class 9 Maths and Ganita Manjari Class 9 Maths Chapter 1 Orienting Yourself The Use of Coordinates Extra Questions, students can improve their problem-solving skills.

Class 9 Orienting Yourself The Use of Coordinates Extra Questions

Extra Questions on Orienting Yourself The Use of Coordinates Class 9

Class 9 Ganita Manjari Chapter 1 Extra Questions

Question 1.
What will be the general form of any point on the x-axis ?
Solution:
The general form of any point on the x-axis is (x, 0).

Question 2.
If the abscissa of a point is x and ordinate is y, then what are the coordinates of the point ?
Solution:
The coordinates of the point are (x, y).

Question 3.
Write the name of horizontal line in a cartesian plane.
Solution:
The name of horizontal line in a cartesian plane is x-axis.

Question 4.
The coordinate axes divide the cartesian plane in how many parts ? What are these parts known as ?
Solution:
The coordinate axes divide the cartesian plane into four parts. These parts are known as quadrants.

Orienting Yourself The Use of Coordinates Class 9 Very Short Question Answer

Question 5.
What is the ordinate of all the points that lie on the x-axis ?
Solution:
The ordinate of all the points that lie on the x-axis is zero.

Question 6.
Write abscissa of following points:
(4, 0), (5, – 3), (- 3, 4) and (0, – 4).
Solution:

Point	Abscissa
(4, 0)	4
(5, – 3)	5
(- 3, 4)	-3
(0, -4)	0

Question 7.
Find the point whose ordinate is 6 and which lies on y-axis.
Solution:
The point whose ordinate is 6 and which lies on y-axis is (0, 6).

Question 8.
What will be the distance of the point (0, – 3) from the origin?
Solution:
Distance of the point (0, – 3) from the origin = 3 units.

Question 9.
If (a, b) = (0, – 2), find the values of a and b.
Solution:
(a, b) = (0, -2)
⇒ a = 0, b = – 2

Question 10.
Perpendicular distance of a point Q from x-axis is 2 units and from y-axis is 5 units. Point Q lies in quadrant III. Write its coordinates.
Solution:
The coordinates of the point Q are (- 5, – 2).

Question 11.
Write any two points lying on the positive direction of y-axis.
Solution:
Tw0 points lying on the positive direction of y-axis can be taken as (0, 1) and (0, 2).

Question 12.
The point (a, b) lies in the IVth quadrant. Which is greater: a or b?
Solution:
Since the point (a, b) lies in the IVth quadrant, therefore
a is + ve
and b is – ve
Clearly, a > b
i.e., a is greater.

Orienting Yourself The Use of Coordinates Class 9 Short Question Answer

Question 1.
In the given figure of a circle, write the coordinates of the points where circle meets the axes.

Solution:
Let the circle meet OX at A and OX’ at A’. Then.
A → (4, 0)
A’ → (- 4, 0)
Let the circle meet OY at B and OY’ at B’. Then.
B → (0,4)
B’ → (0, – 4)

Question 2.
Write coordinates of two points on x-axis and two points on y-axis which arc at equal distances from the origin.
Solution:
The coordinates of two points on x-axis which are at equal distances from the origin can be taken as (1. 0) and (- 1, 0).
The coordinates of two points on v-axis which arc at equal distances from the origin can be taken as (0, 1) and (0, – 1).

Question 3.
If the coordinates of two poins are P(- 2, 3) and Q(- 3, 5). then find (abscissa of P) — (abscissa of Q).
Solution:
(abscissa of P) – (abscissa of Q)
= (- 2) – (- 3)
= – 2 + 3
= 1

Question 4.
Plot the point P(-5, 1) and from it draw PM and PN perpendiculars to x-axis and y-axis respectively. Write the coordinates of M and N.
Solution:

M → (-5, 0)
N → (0, 1)

Question 5.
Write the coordinates of the points X, Y, Z and W from the figure:

Solution:
X → (4, 0)
Y → (4, 3)
Z → (-2, 0)
W → (-2, 4)

Question 6.
With the help of distance formula, show that the points A(4, 2), B(7, 5) and C(9, 7) do not form a triangle.
Solution:
We have
A → (4, 2)
B → (7, 5)
C → (9, 7)
Using distance formula,
AB = \(\sqrt{(7-4)^2+(5-2)^2}\)
= \(\sqrt{(3)^2+(3)^2}\)
= \(\sqrt{9+9}=\sqrt{18}\)
= \(\sqrt{9 \times 2}=3 \sqrt{2}\)

BC = \(\sqrt{(9-7)^2+(7-5)^2}\)
= \(\sqrt{4+4}=\sqrt{8}\)
= \(\sqrt{4 \times 2}=2 \sqrt{2}\)

CA = \(\sqrt{(4-9)^2+(2-7)^2}\)
= \(\sqrt{(-5)^2+(-5)^2}\)
= \(\sqrt{25+25}=\sqrt{50}\)
= \(\sqrt{25 \times 2}=5 \sqrt{2}\)

We find that
AB + BC = 3√2 + 2√2
= (3 + 2)√2
= 5√2 = CA

⇒ The points A. B and C are collincar.
⇒ The points A. B and C do not form a triangle.

Question 7.
If the point P(A: -1, 2) is equidistant from the points A(3, k) and B(k, 5). find the values of k.
Solution:
We have,
P → (- 1, 2)
A → (3, k)
B → (k, 5)
PA = PB
∵ P is equidistant from A and B
⇒ PA² = PB²
∴ (3 – (k – 1))² + (k – 2)² = (k – (k – 1))² + (5 – 2)²
⇒ (3 – k+ 1)² + (k – 2)² = (k – k + 1)² + 3²
⇒ (4 – k)² + (k – 2)² = 1 + 9
⇒ 16 + k² – 8k + k² + 4 – 4k – 10
⇒ 2k² – 12k + 10 = 0
Dividing by 2, k² – 6k + 5 = 0
⇒ k² – 5k – k + 5 = 0
⇒ k(k – 5) – 1(k – 5) = 0
⇒ (k – 5) (k – 1) = 0
Either k – 5 = 0 or k – 1 = 0
i. e., k = 5 or k = 1.

Question 8.
The coordinates of the vertices of ΔABC are A(7, 2), B(9, 10) and C(1, 4). If E and F are the mid-points of AB and AC respectively, prove that EF = \(\frac{1}{2}\)BC
Solution:
We have,
A → (7, 2)
B → (9,10)
C → (1,4)
E is the mid-point of AB
E → \(\left(\frac{7+9}{2}, \frac{2+10}{2}\right)\) [By mid-point formula]
⇒ E → (8, 6)

∵ F is the mid-point of AC
∴ F → \(\frac{1}{2}\)
⇒ F → (4, 3)
Now,
EF = \(\sqrt{(4-8)^2+(3-6)^2}\)
= \(\sqrt{16+9}\)
= \(\sqrt{25}\) = 5 ……….(1)

and BC = \(\sqrt{(1-9)^2+(4-10)^2}\)
= \(\sqrt{64+36}\)
= \(\sqrt{100}\) = 10 ….(2)

From (1) and (2)
EF = \(\frac{1}{2}\)BC.

Question 9.
If the point (x, y) is equidistant from the points (a – b, a + b) and (a + b, a + b), prove that x – a = 0.
Solution:
Let P → (x, y)
A → (a – b, a + b)
and B → (a + b, a + b)
According to the question,
PA = PB
⇒ PA² = PB²
⇒ (x – (a – b)² + (y – (a + b)² = (x – (a + b))² + (y – (a + b))²
⇒ (x – (a – b))² = (x – (a + b))²
⇒ x² + (a – b)² – 2x(a – b) = x² + (a + b)² -2x (a + b)
⇒ a² + b² – 2ab – 2xa + 2xb = a² + b² + 2ab – 2xa – 2xb
⇒ – 2ab + 2xb = 2ab – 2xb
Transposing 4 xb = 4ab
Dividing both sides by 4b, x = a
i.e., x – a = 0.

Orienting Yourself The Use of Coordinates Class 9 Long Question Answer

Question 1.
Write the coordinates of the points A. B. C, D, E and F in the following graph.

Solution:
A → (2, 4)
B → (0, 4)
C → (-3, 2)
D → (-2, 0)
E → (-4, -2)
F → (3, -2)

Question 2.
Write the coordinates of each of the points P, Q, R, S, T and 0 from the adjoining figure.

Solution:
O → (0, 0)
P → (1, 1)
Q → (-3, 0)
R → (-2, -3)
S → (2, 1)
T → (4, -2)

Question 3.
Write coordinates of points A, B, C, D, E and F of figure formed on the graph. Also, write coordinates of * points of intersection of AC and DF with x-axis.

Solution:

A → (-3, 3)
B → (-7, 0)
E → (7, 0)
F → (3, 3)
Coordinates of point of intersection G of AC with x-axis = (- 3, 0)
Coordinates of point of intersection H of DF with x-axis = (3, 0)

Question 4.
Write the coordinates of the points A. B. C and D from the graph. Give points of reflection of A and C in x-axis. Also, give points of reflection of B and D in y-axis.

Solution:
A → (3, 3)
B → (-3, 2)
C → (-6, -2)
D → (2, -5)

Reflection of A in x-axis = E(3, – 3)
Reflection of B in y-axis = G(3, 2)
Reflection of C in x-axis = F(- 6, 2)
Reflection of D in y-axis = H(- 2, – 5)

Question 5.
From the graph, find the coordinates of the points A, B, C, D, E and F. Which points have same abscissas? Also, find which points have same ordinates.

Solution:
A → (0,—3)
B → (4, -5)
C → (6.3)
D → (4, 5)
E → (-6, 3)
F → (-3, 0)
The points B and D have same abscissae
The points C and E have same ordinates.

Orienting Yourself The Use of Coordinates Class 9 Case Based Questions

Question 1.
Observe the graph below and answer the questions that follow :

(i) In the above figure, coordinates of points in second quadrant are
(a) (- 3, 2) and (-2, 3)
(b) (3, 2) and (2, 3)
(e) (3, -2) and (2, -3)
(d) (-3, -2) and (-2, -3)
Solution:
(a) (- 3, 2) and (-2, 3)

(ii) In the above figure. coordinates of points in third quadrant are
(a) (- 3, 2) and (- 2. 3)
(b) (3, 2) and (2, 3)
(c) (3, -2) and (2, -3)
(d) (-3, -2) and (-2, -3)
Solution:
(d) (-3, -2) and (-2, -3)

(iii) In the above figure, coordinates of pomts in fourth quadrant arc
(a) (- 3, 2) and (- 2, 3)
(b) (3, 2) and (2, 3)
(c) (3, -2) and (2, -3)
(d) (-3, -2) and (-2, -3)
Solution:
(c) (3, -2) and (2, -3)

(iv) In the above figure, coordinates of points on y-axis are
(a) (-4, 0) and (3, 0)
(b) (4, 0) and (-3, 0)
(c) (0, -4) and (0, 3)
(d) (0, 4) and (0, -3)
Solution:
(c) (0, -4) and (0, 3)

(v) In the above figure. coordinates of points on x – axis are
(a) (-4, 0) and (3, 0)
(b) (4, 0) and (-3, 0)
(c) (0, – 4) and (0, 3)
(d) (0. 4) and (0, – 3)
Solution:
(a) (-4, 0) and (3, 0)

Orienting Yourself The Use of Coordinates Extra Questions for Practice

Very Short Answers Type Questions

Question 1.
What will be the general form of any point on they-axis?
Solution:
(0, y)

Question 2.
What is the x-coordinate of any point on the y- axis?
Solution:
0

Question 3.
What is the abscissa of the point (- 3, 4)?
Solution:
-3

Question 4.
If ordinate of a point is (- 5) and abscissa is (- 4). write its coordinates.
Solution:
(-4,- 5)

Question 5.
Do P (0, 7) and Q (7, 0) represent the same point?
Solution:
No

Question 6.
Find the point whose ordinate is – 3 and which lies on y-axis.
Solution:
(0,-3)

Question 7.
In which quadrant y-coordinates are negative?
Solution:
III and IV

Question 8.
In which quadrant(s) abscissa of a point is positive?
Solution:
I and IV

Question 9.
On which axis the points P (0, – 4) and Q (0, 4) lie ? What is the perpendicular distance of the point R (- 3, – 4) from x-axis and y-axis ?
Solution:
on y-axis; 4 units: 3 units

Question 10.
Write the distance of point D (3, – 6) from x-axis.
Solution:
6 units

Question 11.
Write the coordinates of the point
(i) whose ordinate is – 5 and which lies on J-axis.
(ii) which lies on x and y axes both.
(iii) whose abscissa is – 3 and which lies on x-axis.
Solution:
(i) (0, – 5)
(ii) (0, 0)
(iii) (- 3, 0)

Question 12.
Without plotting the given points on a graph paper indicate the quadrants in which they lie. if
(a) ordinate = 6, abscissa = – 3
(b) ordinate = – 6, abscissa = 4
(c) ordinate = – 7, abscissa = – 5
(d) ordinate = 3, abscissa = 5
Solution:
(a) IV
(b) II
(c) III
(d) I

Question 13.
Find the coordinates of a point
(i) Whose ordinate is 6 and lies on y-axis.
(ii) Whose abscissa is – 3 and lies on x-axis.
Solution:
(i) (0, 6)
(ii) (-3, 0)

Question 14.
Find the coordinates of a point which
(a) lies on x-axis and is at a distance of 2 units to the left of origin.
(b) lies on y-axis and is at a distance of 4 units above origin.
(c) lies in the second quadrant at a distance of 3 units from x-axis and 2 units fromy-axis.
Solution:
(a) (- 2, 0)
(b) (0, 4)
(c) (- 2, 3)

Question 15.
If a point is on negative side of x-axis at a distance of 5 units from the origin, then find the coordinates of the point.
Solution:
(-5, 0)

Question 16.
P is a point on y-axis at a distance of 6 units from x-axis lying below x-axis. What will be the coordinates of P?
Solution:
P → (0, – 6)

Question 17.
Find the reflection of the point (- 3, – 2) in y-axis.
Solution:
(3, -2)

Question 18.
Find reflection of the point (4, – 4) in x-axis.
Solution:
(4, 4)

Question 19.
Find the reflection of the point (3, 6) in x-axis.
Solution:
(3,-6)

Short Answers Type Questions

Question 1.
If coordinates of a point arc (3, – 10). then write its distances from x-axis and y-axis.
Solution:
10 units and 3 units

Question 2.
Find the distances of points C(- 3, – 2) and D(5, 2) from x-axis and y-axis,
Solution:
Distances of point C(- 3, – 2) from x-axis and y-axis are 2 units and 3 units respectively. Distances of point D(5, 2) from x-axis and y-axis are 2 units and 5 units respectively.

Question 3.
Check if the following points lie on a circle with center (0, 0)
(a) P(5. 12), Q( 13, 0), R(7. 7)
(b) A(3. 4), B(-3. 4), C(0, 5)
Solution:
(a) No;
(b) Yes

Question 4.
The midpoints of the sides of triangle ABC are the points D. E and F, Given that the coordinates of D. E and F ar (0, 4). (4. 5). and (2. —1). respectively, find the coordinates of A. B and C.
Solution:
A(-2, -2), B(2, 10), C(6, 0)

Question 5.
A computer graphics program displays images ‘ on a rectangular screen whose coordinate system has the origin at the bottom-left comer. The screen is 1000 pixels wide and 800 pixels high. A circular icon of radius 90 pixels is drawn with its centre at the point A (100, 80). Another circular icon of radius 60 pixels is drawn w ith its centre at the point B (150, 280).
(a) Does any part of the circle with center as A lie outside the screen?
(b) Check if the two circles intersect each other.
Solution:
(a) Yes; (b) No

Question 6.
Plot the points A(2, 3), B(5, 4), C(6, 9), and D(3, 8) in the coordinate plane. Is ABCD a parallelogram? Justify.
Answer:
Yes

Question 7.
Plot the points A(4, 0), B(0, 3), C(-4, 0). and D(0, -3) in the coordinate plane. Is ABCD a rhombus? Justify. What is the perimeter and area of this rhombus?
Answer:
Yes; 20 units

Long Answer Type Questions

Question 1.
Plot the points A(-2, 1), B(3, 1), C(3, 4). and D(-2, 4) in the coordinate plane. Is ABCD a rectangle? Justify. What is the perimeter and area of this rectangle?
Solution:
Yes; 16 units; 15 sq units

Question 2.
Plot the points A(3, 2), B(0, 3), C(-l, 0). and D(2, -1) in the coordinate plane. Is ABCD a square? Justify. What is the perimeter and area of this square?
Solution:
Yes; 4\(\sqrt{10}\) units; 4\(\sqrt{10}\) sq. units

Question 3.
AB is the diameter of a circle with centre at origin. What are the coordinates of B if coordinates of points A are (3, -4)?
Solution:
B(-3, 4)

Question 4.
Point C(1, 2) lies on the perpendicular bisector of line segment joining the points E(6, 8) and F(2, 4). What is the distance of the point C from the line segment EF.
Solution:
5 units

Question 5.
The base BC of an equilateral triangle ABC lies on y-axis. The coordinates of point C are (0, -3). If the origin is mid-point of the base BC, find the coordinates of the points A and B.
Solution:
B (0, 3), A (0, ±3√3)

Question 6.
If the point P(x,y) is equidistant from the points A(5, 1) and B(-1, 5), prove that 3x = 2y.
Solution:
Since point P(x,y) is equidistant from A(5, 1) and B(−1, 5),
PA = PB
2y = 3x
Hence, Proved

Question 7.
AB is the diameter of a circle whose centre is (2, -3). If the coordinates of B are (1, 4) then find the coordinates of A.
Solution:
B(3, -10)

Question 8.
Three consecutive vertices of a parallelogram arc (-2, -1), (1,0) and (4,3). Find the coordinates of the fourth vertex.
Solution:
(7, 4)

Question 9.
If coordinates of two adjacent vertices of a parallelogram are (3, 2), (1. 0) and diagonals bisect each other at (2, -5), find coordinates of the other two vertices.
Solution:
(1, -12) and (3, -10)

Question 10.
Find the perimeter of the triangle with vertices (0,12), (0, 0) and (5,0).
Solution:
30 units

Case Study Based Questions

In a classroom, four friends Aryan, Vicky, Mann, and Vikas are seated at the points A (3, 4), B (8, 9), C (11, 6) and D (6, 1) respectively.

Based on the above, answer the following questions:
Question 1.
Find the distance between Vicky and Vikas.
Solution:
2√17 units

Question 2.
Find the distance between Aryan and Manu.
Solution:
2√17 units

Question 3.
Show that ABCD is a rectangle.
Solution:
Opposite sides are parallel.
One angle is 90
∠ABC = 90∘

Question 4.
Find the area of rectangle ABCD.
Solution:
30 sq.units